Lateral and Perpendicular Thermal Conductivity Measurement on

Mariusz Felczak,
*Gilbert De Mey,
Bogusław Więcek,
**Marina Michalak
Lateral and Perpendicular Thermal
Conductivity Measurement on Textile Double
Layers
DOI: 10.5604/12303666.1152728
Institute of Electronics,
Lodz University of Technology,
ul. Wolczańska 211-215, 90-924 Łódź, Poland
E-mail: [email protected]
*Department of Electronics
and Information Systems
University of Ghent
Sint Pietersnieuwstraat 41, 9000 Ghent, Belgium
**Department of Material and Commodity Sciences
and Textile Metrology,
Lodz University of Technology,
ul. Wólczańska 211-215, 90-924 Łódź, Poland
nIntroduction
The determination of thermal characteristics of textile has become a very important matter in recent years. Knowledge of
the thermal properties of textiles is not
only important for the design of warm
clothes, but it is also useful to understand
the tactile sensing of fabrics [1 - 5]. Most
investigations are limited to heat transfer
by conduction in the perpendicular direction. In this paper we will focus on thermal diffusion in the lateral direction, i.e.
in the plane of the fabric itself. The new,
so-called smart textiles include several
electronic components having characteristics depending on the ambient conditions, more specifically the temperature.
An electric current flowing through an
electroconductive yarn will give rise to
heat generation which will be mainly
spread in the lateral direction. Hence the
temperature rise can be sensed by electronic components in the neighborhood
of the yarn, which will influence the electrical characteristics. Moreover in the
case of wearable textiles, any temperature increase will be sensed by the human
body as well. The experimental setup
will be used to measure the lateral thermal conductivity in combination with an
analytical model to interpret the results
measured. Afterwards, using a numerical
model, it will be possible to determine
the anisotropic thermal conductivity in a
textile double layer.
The thermal properties of textile materials can also change in time due to moisture diffusion e.g. the existing methods to
investigate thermal properties cannot be
applied to materials with varying thermal
Abstract
In this paper, the temperature distribution on a double layered fleece textile was measured
experimentally with infrared thermography. A theoretical model based on the thin plate
theory was to interpret the results measured. A two dimensional simulation of the same
problem was carried out as well. By fitting the experimental data with the models, thermal
conductivities in the lateral and perpendicular directions could be determined.
Key words: nonwoven, thermal conductivity, heat transfer, anisotropy.
properties. Therefore the authors present
a method based on infrared thermography. The temperature distribution is then
gathered in such a short time that the
eventual variation in the thermal properties can be monitored by taking several
thermal images one after the other.
n Materials used
The process of heat transfer was investigated for needle punched nonwoven sets
prepared by authors. From blends of 40%
flax, 40% steel and 20% polyester, fleeces were produced mechanically using a
carding machine. The linear densities
are, respectively, 47 dtex. (flax), 9 dtex.
(steel) & 1.7 dtex (polyester). The fleeces
were preliminary needled and thermally
pressed at a temperature of 120 °C. The
polyester fibres had a low melting point
so that it was possible to obtain a thin
nonwoven structure. Steel fibres were
inserted to increase the longitudinal thermal conductivity and are the reason for
the nonwoven anisotropy. Moreover additional steel fibres were inserted in part
A of the structure investigated in order to
enable the probe heating (Figure 1).
Morphological and physical properties
of the nonwoven samples were measured
using the standard methods applied to
textile materials. The mass per unit area
was found to be mp = 187 g/m2, the density ρ = 111 kg/m3 and the air permeability Pp = 166.4 cm3/cm2s. The nonwoven
fleece structure has a thickness of about
1.7 mm.
From the nonwoven, fleece samples were
fabricated. Rectangles with dimensions
Felczak M, De Mey G, Więcek B, Michalak M. Lateral and Perpendicular Thermal Conductivity Measurement on Textile Double Layers.
FIBRES & TEXTILES in Eastern Europe 2015; 23, 4(112): 61-65. DOI: 10.5604/12303666.1152728
of 5 × 15 cm were cut in such a way that
the fibres were parallel to the longest
side. On this layer, a second one with dimensions of 5 × 10 cm was deposited and
fixed by needling. As a result the structure shown in Figure 1 was obtained.
Thermal conductivity measurements
were carried out on the double layer, with
a total thickness of 3:4 mm. The single
layer part was used to insert the heating
elements, which were made from steel
yarns, as shown in Figure 1.
n Methods used
A top view of the experimental setup
in shown in Figure 2, where a piece of
fabric was mounted vertically. The first
(thinnest) part AB was heated by an
electric current flowing through electric
conducting yarns made from steel (Figure 1), the aim of which was to warm up
the entire fabric, including the thicker
part BC, which was used for thermographic measurements. With the heat
source being only connected to the thinnest part AB, it would then be possible to
investigate not only the lateral heat transfer (in the x direction) but also the heat
transfer between the two layers constituting the thicker part BC.
Two mirrors were also mounted vertically on both sides of the fabric [19 - 21].
The mirrors were made from aluminium
in order to reflect the infrared radiation.
With an thermographic camera - Cedip
Titanium (USA), infrared radiation was
detected from both sides, and hence the
two temperature distributions T1(x) and
T2(x) could be measured simultaneously
61
Sample
Mirrors
ts = 3.4 mm
X
10 cm
C
Pulse heating
B
5 cm
T2
T1
steel yarns
A
1.7 mm
b = 5 cm
Figure 2. Top view of the experimental setup with the thermographic camera. The two mirrors allow temperature recording on both
sides simultaneously [19].
Figure 1. Isometric view of the structure investigated. Steel yarns
are used for heating.
[6]. Point B, where the thickness changes, was chosen as the origin to display all
experimental results (x = 0). The Cedip
Titanium IR camera is a QWIP (Quantum Well Infrared Photodetector) camera
with an integrated Stirling cooler, which
means that the camera does not have a
shutter, which is used in uncooled microbolometer IR cameras. The shutter usually gets disturbed during IR measurement. The microbolometer camera could
be used if a new shutterless method of
thermal drift compensation was taken
up [7]. The Cedip Titanium has a pixel
resolution of 640 × 512/14 bits, temperature measurement accuracy of ±1 °C or
±1%, and a waveband of 3 - 5 μm. Using thermography with Fourier analysis,
interesting results could also be obtained
[6]. Using these methods, defects and
nonuniformities in the nonwovens could
also be investigated.
50.0
5.0
T1 - T2, °C
T1 + T2, °C
55.0
Experimental results are shown in
Figure 3. Instead of T1(x) and T2(x),
the sum T1(x) + T2(x) and difference
T1(x) - T2(x) are shown. Both curves are,
roughly speaking, exponential decaying
functions. The spreading of lateral heat
(in the x-direction) extends up to a few
millimeters. At the origin x = 0 it was
found that T1(0) = 30 °C or 8 °C above the
ambient (22 °C), whereas T2(0) = 27 °C
or 5 °C above the ambient. In order to
prove the repeatability, a few measurements in the same conditions were made,
one of which was taken for analysis.
In the paper two analyses were conducted. Theoretical analytical calculations
were done using the simple thin sheet
thermal model, which is one-dimensional (Figure 1 and Figure 4.a), whereas
the numerical model in ANSYS is twodimensional (Figure 4.b). Thermal conductivity is calculated for the x and y
direction. The numerical model solves
Kirchoff-Fourier equations for the x and
y direction. Thermal conductivity is anisotropic, thus we calculate kx and ky.
n Theoretical analysis
45.0
x, mm
0.0
5.0
10.0
Figure 3. Experimentally measured temperature distributions. The sum and difference of
the temperatures are displayed to allow easier interpretation.
62
In the theoretical analysis, we will use
the thin sheet thermal model for each layer. Consequently our model will be one
dimensional. Each layer has a thickness
ts, thermal conductivity k and height b.
A top view is shown in Figure 4. The two
sides exposed to ambient air are cooled
convectively, expressed by heat transfer
FIBRES & TEXTILES in Eastern Europe 2015, Vol. 23, 4(112)
be explained further on. Adding and subtracting (1) and (2) yields:
(3)
layer 2
+
layer 1
(4)
a)
or equivalently:
(5)
layer 2
layer 1
b)
(6)
where the characteristic lengths are given
by:
Figure 4. a) Top view of mathematical model, b) view of numerical model – ANSYS.
coefficient h. Heat transfer between the
two layers is expressed by conductance
g in W/m2·K. If there was a third interface layer of thickness t’s and thermal
conductivity k0 in the y direction, one
would have g = k’/t’s. As outlined in the
foregoing section, heat is only supplied
to layer 1. The other layer can only be
heated through the interface, which is described in the model by conductance g.
Nevertheless it is practically impossible
that the second layer will not be heated
directly from the heat source. Hence it
will be assumed that fraction α will be
supplied to layer 2 directly.
According to the thin plate theory, the
differential equations for T1 and T2
are [8]:
20.0
(7)
(1)
(2)
(8)
where T1 and T2 are now temperature
rises above ambient.
To solve Equations 1 and 2, boundary
conditions are needed. First the equations will be replaced by their symmetric components. Later on the boundary
conditions will be provided. It should
be noted here that the boundary conditions are not strictly needed to interpret
the measurements and we only need the
slope of the temperature curves, as will
T1 + T2
(9)
In order to verify these theoretical results, the same data have been plotted
on a semi logarithmic scale, as shown
in Figure 5. The ambient temperature
(22 °C) was subtracted from the experimental values because the model only
provides us with temperatures increases
above the ambient. Both curves can be
0.07
10.0
kx
0.06
5.0
T1 - T2
0.05
k, W/(m.K)
Temperature, °C
The general solutions of (5) and (6) are:
2.0
1.0
0.04
ky
0.03
0.02
0.5
0.01
0.2
x, mm
0.1
0.0
5.0
10.0
Figure 5. Experimentally measured temperature distributions
(semi-logarithmic scale). The sum and difference of the temperatures.
FIBRES & TEXTILES in Eastern Europe 2015, Vol. 23, 4(112)
0.00
0
10
20
30
40
50
iteration
60
70
80
Figure 6. Lateral and perpendicular thermal conductivity kx and ky
as a function of the iteration number.
63
fitted very well to straight lines despite
measurement uncertainties. This proves
that both curves can be represented well
by exponential functions (8) and (9). It is
also clear from Figure 5 that both curves
have almost the same slope, which means
that both characteristic lengths LS and
LD are equal. Consequently the value of
g should be much smaller than the heat
transfer coefficient h due to (7). In other
words, thermal insulation between the
two textile layers is quite high.
Two parallel trendlines have been drawn
in Figure 5, corresponding to characteristic length LS = LD = 2.9 mm.
As the experiments were carried out under
natural convection cooling conditions,
one can assume heat transfer coefficient
h = 8 W/m2·K. Taking radiation into account, one has to add hr = 6 W/m2·K,
which gives rise to a total heat transfer
coefficient of h = 14 W/m2·K. From (7)
we can find the thermal conductivity of
the textile layer:
(10)
where, thickness ts = 1.7 mm was used.
The camera has an accuracy of around 1
°C. As a consequence, the measurements
turn out to be not so accurate for distances x > 5 mm, as can be clearly seen in
Figures 3 & 5.
In order to solve the differential equations, one needs to take into account the
boundary conditions at x = 0. Assuming
that a fraction α of the power supplied P
is fed into layer 2 directly, the major part
(1 − α)P is fed into layer 1:
(11)
(12)
where b is the height of the textile sample. After adding and subtracting (11) and
(12), one gets:
(13)
(14)
Filling in boundary conditions (13) and
(14) in solutions (8) and (9), one obtains:
64
(15)
(16)
Taking into account that LS ≈ LD, one
obtains the following from (15) and (16):
(17)
Experimentally
we
found
that
T1(0) + T2(0) = 13 °C and T1(0) − T2(0)
= 3.5 °C, so that α = 0.37.
n Numerical simulation
For numerical simulation, the same geometry shown in Figures 1 & 4 was
used to carry out a two dimensional thermal analysis. Instead of considering two
separate layers like layer 1 and layer 2
in Figures 1 & 4, a uniform material
with anisotropic thermal conductivity
was considered. The thermal conductivities are now kx in the x direction and ky
in the y-direction. Anisotropy has been
reported in several articles about textile
materials. Anisotropy has been found
in relation to mechanical [9 - 15], optical [16] and electrostatic properties [17].
Also electroconductive screen printed
layers deposited on textile substrates
were found to have anisotropic electric
conductivities [18]. It was proved that the
anisotropy was due to the structure of the
textile itself and not to the conducting ink
screen printed on it. Hence it is quite reasonable to accept anisotropic behaviour
for the thermal conductivity.
Thermal simulations were carried out using the ANSYS software package. The
program delivers two temperature distributions T1(x) and T2(x) on both sides of
the nonwoven structure. This simple heat
transfer problem is used to find the solution of the inversed heat transfer problem. The simple heat transfer problem receives the boundary conditions (thermal
conductivity, density etc.) and outputs
the temperature distribution.
The inverse heat transfer problem as the
input values receives the temperature
distribution and some of the boundary
conditions or material parameters [22].
Depending on the inverse heat transfer
problem solution method, using the temperature measured for one or more parameters can be determined. In the paper,
it is thermal conductivity.
In this study, the inverse heat transfer
problem was solved using the simple
heat transfer model and optimisation
programme created in Matlab® software.
For optimisation, the algorithm golden
cut method was used. The root mean
square of temperatures (experimental and
simulated) is minimised.
For the first simulation, arbitrary values
for kx and ky were inputted to the optimisation program. The resulting temperature distributions are introduced automatically form the ANSYS® thermal solver
to the main optimisation program. Then
they are compared with the experimental
values (root mean square error is calculated). In each iteration of the optimisation, new values of thermal conductivity
are introduced to ANSYS®. Using the
optimisation programme, it was possible
to determine the thermal conductivity.
The iterations were repeated till sufficient convergence was obtained. Figure 6 shows the values of kx and ky as
a function of the number of iterations.
A nice convergence is observed towards values kx = 0.0628 W/m·K and
ky = 0.0268 W/m·K, clearly showing
the anisotropic behaviour. During the
ANSYS simulation, heat transfer coefficient h = 8 W/m2·K was used and also
heat transfer by radiation, which corresponds to total heat transfer coefficient
h = 14 W/m2·K, the same value as in the
theoretical section. It should be mentioned here that the simulation result
for kx agrees very well with the value
k = 0.0688 W/m·K obtained from the
theoretical model outlined in the previous section. It should also be noted that
the value ky = 0.0268 W/m·K is very low,
comparable with the thermal conductivity of most insulating materials. In the
theoretical section, the conductivity in
the y direction was found to be almost
zero, which is due to the fact that a simpler model was used, whereas the ANSYS simulation was a fully two dimensional analysis.
FIBRES & TEXTILES in Eastern Europe 2015, Vol. 23, 4(112)
nConclusion
Thermographic measurements were carried out on a piece of textile made from a
double layered fleece material. One of the
layers was heated, whereas the other one
could only be heated through conduction
from the first one. A theoretical model
was set up for this textile structure and
the results compared with the experimental data. It was found that the perpendicular conduction was almost non-existant.
The lateral thermal conductivity was
found to be k = 0.0688 W/m·K. With ANSYS software a two dimensional simulation was carried out as well. The lateral
and perpendicular thermal conductivities
were found to be kx = 0.0628 W/m·K and
ky = 0.0268 W/m·K, respectively. The
conclusion is that the simple analytical
model is suited to determine the lateral
thermal conductivity. To measure both
conductivities, a more detailed two dimensional model is required. It should
be noted that the temperature drops at a
length constant at around 3 mm. Hence
only a small area is suited for measurements, which is not a problem if thermography is used.
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Aachen-Dresden International
Textile Conference 2015
26-27.11.2015, Aachen, Germany
Partner country: France.
The “Aachen-Dresden” is one of
the most important textile meetings in Europe. It addresses experts
in the fields of textile chemistry,
finishing and functionalisation, as
well as textile machinery, manufacturing and composites within the
following topics:
n Bioactive and biomimetic materials
n Biotechnology and bioprocessing
n Fibre technology
n Sustainability and bio-based
building blocks
n Flexible electronics
Organizers:
n DWI - Leibniz Institute for
Interactive Materials, Aachen
n Institute for Textile Machines
and Techniques for HighTech Textile Materials of the
Technical University Dresden,
ITM with Its Friends’ and
Promotion Society
in cooperation with:
n DTNW, German Centre for
Textile Research Nord-West,
Krefeld
n Faculty for Textile and Clothing
Technique of the University
Niederrhein, Mönchengladbach
n IfN, Institute for Sewing
Technique, Aachen
n IPF, Leibniz Institute for
Polymer Investigation, Dresden
n ITA, Institute for Textile
Technique of the RWTH
Technical University Aachen
n ITMC, Institute for Technical
and Macromolecular Chemistry
of the RWTH Technical
University Aachen
n STFI, Textile Research Instittute
of Saxonia, Chemnitz
n TFI, German Research Institute
for Geosystems, Aachen
n TITV, Thüringen-Vogtland
Textil Research Institute, Greiz
supported as well by:
n The Board of Trustees for
Researchers of Textiles, Berlin
For further information:
http://aachen-dresden-itc.de
Reviewed 13.02.2015
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